Six colleges – A, B, C, D, E and F – jointly conducted an entrance exa…

Question

Six colleges – A, B, C, D, E and F – jointly conducted an entrance examination. The exam had four sections – I, II, III and IV. The following table gives the sectional cut-off marks specified by the colleges and the overall cut-off marks. A student will get a call from a college only if he/she scores at least the sectional and overall cut-off marks specified by that college. The maximum marks in each section is 50.

| Section → College ↓ | I | II | III | IV | Overall |
|---|---|---|---|---|---|
| A | 40 | – | – | 43 | 160 |
| B | – | 40 | 42 | 45 | 168 |
| C | 41 | – | 43 | – | 165 |
| D | – | 45 | – | 42 | 170 |
| E | 43 | – | 45 | – | 175 |
| F | – | 43 | – | 40 | 167 |

(A '–' means no cutoff is specified for that section by that college.)

**Q1.** Anuj did not get a call from any of the colleges. What is the maximum marks he could have scored?

Accepted Answer

A. 181

To miss every college Anuj must violate at least one cutoff for each one. To MAXIMISE total he should keep two sections at 50 and tank the other two as efficiently as possible.
Best pair: section III = 42 and section IV = 39.
- A (IV ≥ 43): 39 < 43 ✗ fails
- B (IV ≥ 45): 39 < 45 ✗ fails
- C (III ≥ 43): 42 < 43 ✗ fails
- D (IV ≥ 42): 39 < 42 ✗ fails
- E (III ≥ 45): 42 < 45 ✗ fails
- F (IV ≥ 40): 39 < 40 ✗ fails
Maximum total = 50 + 50 + 42 + 39 = 181.

Answer

180

Answer

155

Answer

159